Right Bol Loop 16.9.2.237 of order 16


0123456789101112131415
1151413121190102845367
2141511131009121583476
3131115914121005762148
4121090151311148617235
5111314150101293271684
6901210131514117438512
7091011121415136354821
8101201491113154126753
9215387640111310121514
1035162487120149151113
1148671352139015141012
1253217846101415091311
1384726531111591401210
1467483125151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   10   13   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

9 Elements of order 2:   4   5   9   10   11   12   13   14   15

6 Elements of order 4:   1   2   3   6   7   8

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,8)(10,13) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001